Let us assume a local Cartesian frame centered in one of the plates and two
different orientations of the Casimir apparatus. The first with the \(x\)  axis
being perpendicular to the plates, which we call the \(x\) -orientation, note
that this is the orientation considered in Ref. [1]}, [2]}. The second
one with the \(y\)  axis being perpendicular to the plates, which we call the
\(y\) -orientation. In what follows we call \(\xi \)  the coordinate perpendicular to
the plates, then we can generally refer to the \(\xi \) -orientation.
